ENGLISH

Fields and rings

By Irving Kaplansky

Book information

Publisher
The University of Chicago Press
Year
1972
ISBN
0226424502, 0226424510
Language
english
Format
PDF
Filesize
11 MB (11283945 bytes)
Series
Chicago Lectures in Mathematics
Edition
2
Pages
\216
Topic
Mathematics Algebra
Time added
2022-03-28 23:22:10

Description

Title Contents Preface to the second edition Preface to the first edition Part I. Fields 1. Field Extensions 2. Ruler and compass constructions 3. Foundations of Galois Theory 4. Normality and Stability 5. Splitting Fields 6. Radical Extensions 7. The Trace and Norm Theorems 8. Finite Fields 9. Simple Extensions 10. Cubic and Quartic Equations 11. Separability 12. Miscellaneous results on radical extensions 13. Infinite Algebraic Extensions Part II. Rings 1. The Radical 2. Primitive Rings and the Density Theorem 3. Semi-Simple Rings 4. The Wedderburn Principal Theorem 5. Theorems of Hopkins and Levitzki 6. Primitive Rings with Minimal Ideals and Dual Vector Spaces 7. Simple Rings Part III. Homological Dimension 1. Dimension of modules 2. Global dimension 3. First theorem on change of rings 4. Polynomial rings 5. Second theorem on change of rings 6. Third theorem on change of rings 7. Localization 8. Preliminary lemmas 9. A regular local ring has finite global dimension 10. A local ring of finite global dimension is regular 11. Injective modules 12. The group of homomorphisms 13. The vanishing of Ext 14. Injective dimension Notes Bibliography for the notes Index

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